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A166597
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Let p = largest prime <= n, with p(0)=p(1)=0, and let q = smallest prime > n; then a(n) = q-p.
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2
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2, 2, 1, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 2, 2, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Note the large prime gap of 72 between 31397 and 31469. This is the prime gap with the largest merit (cf. A111870), 72/log(31397)=6.95352 for primes less than 100000. Also 72/(log(31397))^2=0.67154 (cf. conjectures of Cramer-Granville, Shanks and Wolf) is largest for primes less than 100000. [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
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LINKS
| Daniel Forgues, Table of n, a(n) for n=0..100000
Eric Weisstein's World of Mathematics, Prime Gaps. [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
Eric Weisstein's World of Mathematics, Cramer-Granville Conjecture. [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
Eric Weisstein's World of Mathematics, Shanks Conjecture (and Wolf Conjecture.) [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
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EXAMPLE
| a(0)=2 since the least prime greater than 0 is 2 (gap of 2 from 0 to 2.)
a(9)=4 since the least prime greater than 9 is 11 (gap of 4 from 7 to 11.)
a(11)=2 since the least prime greater than 11 is 13 (gap of 2 from 11 to 13.)
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MATHEMATICA
| f[n_]:=Module[{a=If[PrimeQ[n], n, NextPrime[n, -1]]}, NextPrime[n]-a]; Join[{2, 2}, Array[f, 120, 2]] (* From Harvey P. Dale, May 17 2011 *)
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CROSSREFS
| Cf. A151800, A166594.
Cf. A111870 [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
Sequence in context: A194822 A029405 A029350 * A000003 A168208 A197081
Adjacent sequences: A166594 A166595 A166596 * A166598 A166599 A166600
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KEYWORD
| nonn
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AUTHOR
| Daniel Forgues (squid(AT)zensearch.com), Oct 17 2009
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EXTENSIONS
| Comment, links and cross-reference added by [From Daniel Forgues (squid(AT)zensearch.com), Oct 23 2009]
Definition rephrased by N. J. A. Sloane, Oct 25 2009
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